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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 495, page id 1815201908:0552
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=552
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 80 lines, status machine
# Lines: 80 recognised, mean confidence 0.80
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

Keur.
AB
S,T,
lA
X hy.
EAD
IHO
EAH
Ou
igieur
N. A.
pro.
AR.
SiLP.
BC.
BuEm
alum
arum
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rSula
AF
Lol
le
inex
2
ve
Cum
ecta
se
Had
tra.
1
D.
P AR A BOL A.
PR OPOSTTIO CCZOIZ.
AEmicireulum ABC CCCEF
Dorthosoalicer in D di2-
meeri dux AC, BD. Pona-
cur aucem FE linca parallela
AC: dem lumpris in AC
punctis FF, Cliganeurnorma-
les FE, OCCMILenTES PF linca
in C, Cemicheuto in C6. Fane 
ducem proporcionales F F:
Dico H, E, C puncta este
CF, ElF.
adparabolam.
Demonstratio.
Vn enim proporcionales sine
FL, OF, HIL, eric vequadra-
cum FC ad quadracum F C, SC AC
EFH rectangulum ad rectangu-
lum FF FI: led F: F FT rectangula illam inter Sc habent FatroneM, quam MnCx LIF,
igicur ex HIF linex lunc re quadeata CF: id est Ve AF C rectangula, puncta ixieur
H, FI, C ad parabolam LunE.
Idem conringet in ellixsi, si A C. B D diametri ponantur coniueata, et F. F aequi distantes
ipsi BD.
P ROP OSIFIO CCC.
Fomentum circuli A BC subrendat recta AC, quam in D Sccent
quorcunque D F, parallelae contingenti F. G per A ductae: Rac au=
cemi vE AB ad AB, sICD F. ad DF.
Dico A, E, F. puncta ese ad parabolam.
Demonstratio.
Vngancur AB, B C: quoniam FG contin-
oens eR, angulus C AG equatur anoulo
ABC; sed angulo C A C: aequalis est ansu-
IuS ADB, quia F G, D F xequidictane; an:
suloigicur ABC aequalis est anguluS ADB;
ex crianpula AB C, A BD, Cimilia Punc. qua-
ReVE AD ad AB, lic AB ad AC; _D AC
rectansulo aquale est quadratum AB. qua-
dratum isitur AB est ad quadratum AB, vE
D AC rectangulum ad rectangulum D AC.
id cst v= D A linca ad lineam D A: sed AB
quadraris aqualia sune quadrata DF,, qua-
drata icsieur D P eam habene rationem, quam
obcinenclinex D A. quare AF, C puncta ad
parabolam CuNF.
eRO:
rit